1. Field of the Invention
The present invention relates to a method for measuring a profile of a roll, and more particularly, to a method capable of measuring the profile of a roll in an in-line mode on a rolling mill for making a sheet, such as a hot rolling mill.
2. Description of the Related Art
It is generally known in a rolling mill for making a sheet, such as a hot rolling mill, that a work roll wears locally at its service face, which comes into contact with a workpiece to be rolled out. To obtain a sheet with a uniform distribution of thickness, therefore, the order of rolling workpieces must be controlled such that the workpieces must be passed along a rolling line in the order of decreasing width. However, this control on the order of rolling workpieces by their widths is a significant impediment to increased productivity. To eliminate the control on the order of rolling, a proposal has been made for so-called on-line roll grinding means. This type of grinding means grinds the service surface of a worn work roll to a desired configuration, with the work roll in an in-line state incorporated in a roll mill stand. The most important task in performing this work roll grinding is to monitor the profile of the work roll to be ground, before, after, and during the grinding operation.
A conventional method for measuring the profile of a roll is disclosed, for example, in Japanese Patent Publication No. 15970/94. The earlier technology will be described with reference to FIG. 14. In FIG. 14, the reference numeral 1 denotes a housing, and a work roll 2 is disposed in the housing 1. Below the work roll 2, a plurality of displacement detectors 3a to 3g are placed, and a displacement detector mount 4 is disposed for supporting these displacement detectors 3a to 3g. The displacement detector mount 4 is slidably engaged on a guide rail 6 attached to a support beam 5. The displacement detector mount 4 is adapted to move in the axial direction of the work roll 2 when a threaded shaft 7 is driven by a motor 8. The support beam 5 has opposite ends, in a longitudinal direction thereof, supported slidably on guides 9 of the housing 1, and is provided with a pair of positioning arms 10 projecting from a surface thereof facing the work roll 2. The opposite (lower) surface of the support beam 5 is joined to a pair of cylinders 11 attached to the housing 1 or a pedestal. The sliding surface of the guide rail 6 is held nearly parallel to the axial direction of the work roll 2 when the cylinders 11 press the support beam 5 against the lateral ends of the work roll 2 via the positioning arms 10. The reference numerals 12a to 12e denote displacement detector support tubes, which bear the displacement detectors 3a, 3b, (3c, 3d, 3e), 3f and 3g, respectively, and are movable toward and away from the work roll 2. The displacement detectors 3a to 3g are disposed opposite and facing the surface of the work roll 2 and nearly perpendicularly to the axis of the work roll 2 to measure surface irregularities of the work roll 2. During a measuring operation, the displacement detectors 3a to 3g are jutted toward the work roll 2 by a predetermined distance by means of the support tubes 12a to 12e.
According to the earlier technology constituted as described above, the support beam 5 is brought into pressed contact with the surface of the work roll 2 through the positioning arms 10 by the cylinders 11. In this state, the displacement detector mount 4 is moved in the axial direction of the work roll 2, so that the profile of the work roll 2 can be measured by the displacement detectors 3a to 3g. This profile measuring method of the earlier technology, however, has the following problems:
First, the guide rail 6 must extend straight and nearly parallel to the axial direction of the work roll 2 for the measuring operation. However, if the guide rail 6 deforms or waves, the amount of its deformation or waving is added to the measured data provided by the displacement detectors 3a to 3g. Thus, the true surface irregularities of the work roll 2 cannot be measured. Particularly when the above-described measuring method is applied to a hot rolling mill, the guide rail 6 thermally deforms under the influence of heat during rolling, thus making it difficult to measure irregularities of the roll surface with high accuracy.
The second problem is encountered when carrying out the above profile measuring method during hot rolling work (i.e., when it is designed to measure the surface of the work roll 2 at positions on a generator of the roll barrel on the basis of a pulse signal synchronous with the rotation of the work roll 2). In this case, not only errors due to the deformation or waving of the guide rail 6, but also excessive play between roll bearing housings (not shown) and the housing 1, excessive play between roll bearings (not shown) and roll journals (not shown), and the whirling motion of the work roll 2 due to the eccentric rotation of a backup roll are added to the measured values provided by the displacement detectors 3a to 3g. Thus, the true surface irregularities of the work roll 2 cannot be measured. That is, the measured values, provided by the displacement detectors 3a to 3g, include the true values of irregularities in the surface of the work roll 2, errors caused by errors in the motion of the displacement detector mount 4, and errors in the rotation of the work roll 2 during measurement.
In an attempt to solve these problems, Japanese Patent Publication No. 15970/94 discloses a high accuracy, roll profile measuring method achieved by using a processing procedure to be described in detail below. The earlier technology of this publication will be described with reference to FIG. 3. FIG. 3 is an excerpt from FIG. 14 (3c, 3d, 3e and 12c).
In FIG. 3, L.sub.b and L.sub.a represent the center distances between the displacement detectors 3c and 3d and between the displacement detectors 3d and 3e, respectively. x represents the abscissa of the position of the displacement detector mount 4 that has moved in the axial direction of the work roll 2, m(x) represents the profile of the work roll 2, e.sub.z (x) represents a relative translational motion error component caused by the relative translation of the displacement detector support tube 12c and the work roll 2 due to errors caused by the movement of the displacement detector mount 4 and the rotation of the work roll 2, and e.sub.p (x) represents a relative pitching motion error component attributed to similar causes.
Outline of Processing Procedure
(i) Let the roll profile, translational motion error, and pitching motion error at a position at a moving distance x.sub.n from a measurement starting position be m(x.sub.n), e.sub.z (x.sub.n) and e.sub.p (x.sub.n), respectively. Measured values y.sub.3c (x.sub.n), y.sub.3d (x.sub.n) and y.sub.3e (X.sub.n) provided by the displacement detectors 3c, 3d and 3e, respectively, are expressed by: EQU y.sub.3c (x.sub.n)=m(x.sub.n -L.sub.b)-e.sub.z (x.sub.n)-L.sub.b .multidot.e.sub.p (x.sub.n) EQU y.sub.3d (x.sub.n)=m(x.sub.n)-e.sub.z (x.sub.n) EQU y.sub.3e (x.sub.n)=m(x.sub.n +L.sub.a)-e.sub.z (x.sub.n)+L.sub.a .multidot.e.sub.p (x.sub.n) (1)
(ii) Measured values y.sub.3c (x.sub.n), y.sub.3d (x.sub.n) and y.sub.3e (x.sub.n) (n=0, 1, 2, . . . , N-1) provided by the displacement detectors 3c, 3d and 3e are weighted and added as in Equation (2) to obtain a composite measured value Y(x.sub.n) not affected by the motion errors e.sub.z (x.sub.n) and e.sub.p (x.sub.n) (i.e., data in which the terms concerning the motion errors e.sub.z (x.sub.n) and e.sub.p (x.sub.n) have been eliminated) ##EQU1##
(iii) A stream of composite measured data Y(x.sub.n) (n=0, 1, 2, . . . , N-1) is subjected to Fourier transformation by using Equation (3) to obtain a roll profile m(x.sub.n) (n=0, 1, 2, . . . , N-1). (Hereinafter, a method of measuring the roll profile m(x.sub.n) by using Equation (3) will be referred to as "the three-point method".) ##EQU2## where F.sub.k : Kth order coefficient of the cosine component of an expression obtained by the Fourier transformation of the data stream Y(x.sub.n)
G.sub.k : Kth order coefficient of the sine component of an expression obtained by the Fourier transformation of the data stream Y(x.sub.n) ##EQU3## .delta..sub.k : tan.sup.-1 {a.multidot.sin K.alpha.-b.multidot.sin K.beta.)/(1+a.multidot.cos K.alpha.+b.multidot.cos K.beta.)} PA1 .alpha.: 2.pi.L.sub.a /L PA1 .beta.: 2.pi.L.sub.b /L PA1 L: Measured length of an object to be measured PA1 a: -L.sub.b /(L.sub.a +L.sub.b) PA1 b: -L.sub.a /(L.sub.a +L.sub.b)
(iv) From Equations (3) and (1), the errors e.sub.z (x.sub.n) and e.sub.p (x.sub.n), at the time of measurement, are calculated.
(v) The measured data at the displacement detectors 3a, 3b, 3d, 3f and 3g are corrected with the errors e.sub.z (x.sub.n) and e.sub.p (x.sub.n) to obtain the ideal measured values free from motion errors (i.e., the true fractional roll profiles). These corrected measured values are combined to obtain the entire roll profile.
The roll profile measuring method disclosed in Japanese Patent Publication No. 15970/94 eliminates the effect of the errors e.sub.z (x.sub.n) and e.sub.p (x.sub.n). Thus, this method is suitable for achieving accurate measurement by using, for example, the displacement detector mount 4 in an actual rolling mill that is difficult to move with high accuracy. However, this method still has the following problems:
According to the three-point method, with an increase in the moving distance L of the displacement detector mount 4 during roll profile measurement, shape evaluation errors of low K orders, such as first order and second order, in Equation (3) tend to occur. This drawback will be outlined below.
As shown in Equation (3), when determining the roll profile m(x.sub.n) (its Kth order component), a multiplication using a constant 1/f.sub.k specific to the measuring system is executed. Generally, the measured data y.sub.3c (X.sub.n), y.sub.3d (X.sub.n), and y.sub.3e (X.sub.n) at the displacement detectors 3c, 3d, and 3e include a measurement noise, and the coefficients F.sub.k and G.sub.k obtained by the Fourier transformation of the composite measured data stream Y(x.sub.n) (n=0, 1, 2, . . . , N-1) also include evaluation errors .DELTA.F.sub.k and .DELTA.G.sub.k, respectively. Accordingly, in the roll profile m(x.sub.n) (its Kth order component), the evaluation errors .DELTA.F.sub.k and .DELTA.G.sub.k are multiplied by 1/f.sub.k, thus exerting influence. Suppose, here, that L.sub.a =L.sub.b for simplicity. Then, from Equation (3), the value of 1/f.sub.k for low-order modes (i.e., modes in which K takes a small value such as 1 or 2) can be approximately expressed by Equation (4): EQU 1/f.sub.k .apprxeq.2/(2.pi.K).sup.2 .multidot.(L/L.sub.a).sup.2(4)
Table 1 shows the values of f.sub.k when L.sub.a =L.sub.b =22 mm and L=1024 mm by way of example. As is obvious from Table 1, when the evaluation error .DELTA.G.sub.1 =1 occurs, the first order sine component of the roll profile m(x.sub.n) includes an error of 1/0.0091.apprxeq.110.
TABLE 1 __________________________________________________________________________ Value of f.sub.k (K = 1 to 100) (L.sub.a = L.sub.b = 22 mm, L = 1024 mm) 1 2 3 4 5 6 7 8 9 10 __________________________________________________________________________ 0 .00910 .03622 .08089 .14227 .21926 .31046 .41420 .52860 .65158 .78090 10 .91420 1.04907 1.18304 1.31368 1.43862 1.55557 1.66242 1.75721 1.83822 1.90399 20 1.95331 1.98528 1.99932 1.99518 1.97294 1.93299 1.87607 1.80321 1.71573 1.61523 30 1.50354 1.38268 1.25487 1.12241 .98773 .85327 .72148 .59476 .47541 .36561 40 .26735 .18242 .11236 .05846 .02168 .00271 .00188 .01921 .05439 .10677 50 .17541 .25905 .35617 .46500 .58357 .70971 .84114 .97546 1.11022 1.24298 60 1.37131 1.49290 1.60551 1.70711 1.79584 1.87009 1.92851 1.97003 1.99391 1.99970 70 1.98730 1.95694 1.90917 1.84485 1.76517 1.67156 1.56573 1.44961 1.32531 1.19509 80 1.06132 .92643 .79288 .66311 .53946 .42419 .31939 .22699 .14864 .08579 90 .03957 .01082 .00008 .00752 .03303 .07612 .13603 .21166 .30163 .40431 __________________________________________________________________________
The present invention has been made in an attempt to solve the above-described problems with the earlier technology. It is an object of the present invention to provide a method for measuring a roll profile with high accuracy by suppressing the occurrence of shape evaluation errors of low-order modes.
Another object of the present invention is to provide a method for measuring a roll profile with high accuracy by suppressing the occurrence of shape evaluation errors of not only low-order modes but also high-order modes.
Still another object of the present invention is to provide a method for measuring a roll profile with high accuracy by decreasing measurement noise related to shape evaluation errors of low-order modes while eliminating motion errors during the measurement of the roll profile.
A further object of the present invention is to provide a roll profile measuring method capable of measuring the profile of a long roll with high accuracy and efficiently.